---
title: "Population Aging and the Fiscal Sustainability Trap: Expenditure Asymmetry, Debt Dynamics, and the Limits of the Interest Rate Channel"
author: "Working Paper"
date: "February 2026"
abstract: |
  Does population aging undermine fiscal sustainability? We test this using the Bohn (1998) fiscal reaction function framework across 181 countries from 1990 to 2024, incorporating Fair-Dominguez demographic polynomials. The baseline Bohn coefficient is positive but small (0.005, p = 0.043), confirming weak fiscal discipline in the pooled sample. When estimated on the cyclically-adjusted structural balance, the coefficient reverses sign (-0.011, p = 0.005), a sign reversal that is robust across alternative gap measures though statistical significance varies with the gap construction. Rolling-window estimation reveals that the Bohn coefficient was negative in the 1990s, turned positive during 2001--2018, and has collapsed to insignificance since 2020. However, demographics do not weaken the Bohn coefficient through the interaction channel. Instead, aging operates through a stark expenditure-revenue asymmetry: a 10 percentage point increase in the old-age dependency ratio raises government expenditure by approximately 13 percentage points of GDP but revenue by only 4 points, opening a fiscal gap of approximately 6 points of GDP per unit OADR. This gap is 80% non-health (pensions, social transfers), contradicting the common emphasis on healthcare costs. Demographics strongly predict interest rate levels (Z_1 on rates: -55.6, p = 0.001) but not the interest-growth differential (r-g): the nominal r-g effect is insignificant (p = 0.44), and on a homogeneous 23-country bond yield sample r-g remains null (p = 0.48). Demographics are strongly associated with debt accumulation through the fiscal gap (Z_1 coefficient on debt change: +20.6, p = 0.005). No-policy-change mechanical projections through 2040, with Monte Carlo uncertainty bands and stylized Bohn policy reactions, show that most major economies face rising debt trajectories under current demographic trends, underscoring the urgency of pension reform.
keywords: "fiscal sustainability, demographics, aging, Bohn test, fiscal dominance, debt dynamics, pension spending"
jel: "H63, H55, J11, E62"
bibliography: references.bib
---

# Introduction

Government debt ratios across the advanced world have reached peacetime records. The United States surpassed 120% of GDP in 2024, France exceeded 117%, and Japan remains above 224%. These debt levels coincide with an unprecedented demographic transition: the populations of these same countries are aging rapidly, with old-age dependency ratios projected to double in many economies by 2060. The question is whether these two trends are connected---whether aging systematically undermines the fiscal discipline that keeps public debt sustainable.

The theoretical case for demographic fiscal stress operates through multiple channels. First, aging directly increases age-related public spending---pensions, healthcare, long-term care---creating persistent primary deficits [@lee2003; @yared2019]. Second, aging may depress the natural rate of interest through lifecycle savings effects [@carvalho2016; @rachel2017], but simultaneously reduce potential growth, with the net effect on the interest-growth differential (r-g) determining debt dynamics [@blanchard2019]. Third, as debt accumulates, the fiscal reaction function itself may weaken: governments facing aging electorates may find it politically impossible to tighten fiscal policy in response to rising debt, creating what @sargent1981 termed "fiscal dominance"---a regime in which monetary policy is subordinated to fiscal requirements.

Despite this rich theoretical structure, there is no systematic cross-country empirical test of whether demographics predict the breakdown of fiscal sustainability. @bohn1998 established the standard test: if the primary balance responds positively to lagged debt ($\beta > 0$), the government's intertemporal budget constraint is satisfied and debt is sustainable. @ghosh2013 extended this to show "fiscal fatigue"---the response weakening at high debt levels---but did not incorporate demographics. @katagiri2020 modeled aging and fiscal sustainability theoretically for a small open economy, and @plantin2024 analyzed fiscal dominance regimes, but neither tested the demographic channel empirically across a broad country panel.

This paper fills that gap. We estimate the Bohn fiscal reaction function for 181 countries over 1990--2024, using Fair-Dominguez demographic polynomials [@fair1991] to capture the full age distribution. We test whether aging weakens the Bohn coefficient, decompose the channels through which demographics affect debt sustainability, and project forward debt trajectories under current demographic trends.

Our results yield a clear and surprising conclusion: **aging threatens fiscal sustainability, but through the spending channel, not the interest rate channel**. The key findings are:

1. **The Bohn coefficient is positive but fragile.** The pooled primary-balance reaction to lagged debt is +0.005 (p = 0.043) across 181 countries. But estimated on the structural balance, which strips out automatic stabilizers, the coefficient reverses sign to -0.011 (p = 0.005). This sign reversal is robust across alternative gap measures, though statistical significance varies with the gap construction.

2. **Demographics do not weaken the Bohn coefficient directly.** Interaction terms between lagged debt and demographic polynomials are insignificant (all p > 0.41). Aging does not operate by eroding the fiscal reaction function---it operates by making the fiscal environment worse.

3. **The expenditure-revenue asymmetry is the core mechanism.** A 10 percentage point increase in the old-age dependency ratio raises government expenditure by approximately 13 points of GDP but revenue by only 4 points, opening a structural fiscal gap. This 3.3:1 asymmetry is 80% driven by non-health spending (pensions and social transfers), not healthcare.

4. **We do not find robust evidence that demographics move the r-g differential.** Demographics strongly predict interest rate levels (Z_1 = -55.6, p = 0.001) but the effects on rates and growth approximately cancel in the nominal r-g differential (p = 0.44). On a homogeneous 23-country bond yield sample, r-g remains insignificant (p = 0.48). The theoretical worry that aging raises r-g and accelerates debt spirals is not robustly supported.

5. **Demographics are strongly associated with debt accumulation.** The Z_1 coefficient on annual debt change is +20.6 (p = 0.005): aging countries accumulate debt faster, controlling for the fiscal balance, interest rates, and growth.

6. **Most major economies face rising debt trajectories.** No-policy-change mechanical projections through 2040, with Monte Carlo uncertainty bands, show median debt-to-GDP ratios exceeding 200% for the United States, United Kingdom, France, China, and India. Even with a stylized Bohn policy reaction ($\beta = 0.02$), most trajectories remain on upward paths.

The remainder of this paper proceeds as follows. Section 2 reviews the literature on fiscal sustainability and demographics. Section 3 describes the data. Section 4 presents the Bohn test results and expenditure decomposition. Section 5 examines r-g dynamics. Section 6 presents debt trajectory simulations. Section 7 provides robustness checks. Section 8 concludes.


# Literature Review

## Fiscal Sustainability and the Bohn Test

The modern empirical framework for fiscal sustainability derives from @bohn1998, who showed that a positive response of the primary balance to the debt-to-GDP ratio ($\beta > 0$ in $pb_t = \beta d_{t-1} + \gamma X_t + u_t$) is sufficient to ensure that the government's intertemporal budget constraint is satisfied. This test has become the standard in the literature, with @bohn2007 establishing its theoretical properties and @mauro2015 applying it across a long historical panel.

@ghosh2013 introduced the concept of "fiscal fatigue": while the primary balance initially responds positively to rising debt, the response weakens and eventually reverses at very high debt levels, defining a "fiscal limit" beyond which sustainability is not assured. Their estimated reaction function for advanced economies implies that several countries---notably Japan and Italy---have approached or exceeded their fiscal limits. However, Ghosh et al. do not incorporate demographic variables, treating the fiscal reaction function as time-invariant conditional on controls.

## Demographics, Interest Rates, and Growth

A parallel literature examines how demographics affect the components of the debt accumulation identity $\Delta d_t = (r_t - g_t) d_{t-1} - pb_t$. @carvalho2016 develop an overlapping-generations model in which aging depresses the equilibrium real interest rate by increasing the savings supply relative to investment demand. @rachel2017 estimate that demographics account for roughly 90 basis points of the secular decline in global real rates. @summers2014 frames this as "secular stagnation"---chronically insufficient demand in aging economies.

The net effect of demographics on the r-g differential is theoretically ambiguous. Aging depresses both the natural rate of interest (lowering r) and potential growth (lowering g). If the interest rate effect dominates, r-g falls and debt dynamics become more favorable; if the growth effect dominates, r-g rises and debt sustainability worsens. @blanchard2019 argues that the current environment of r < g in many advanced economies makes public debt less costly than traditionally assumed, but notes that this may not persist as demographic pressures intensify.

## Demographics and Fiscal Dominance

@sargent1981 first described "unpleasant monetarist arithmetic": when fiscal policy does not adjust to stabilize debt, monetary policy must eventually monetize the deficit, regardless of the central bank's preferences. @leeper1991 formalized this as a regime distinction between "active" monetary policy (where the central bank controls inflation) and "active" fiscal policy (where the fiscal authority does not adjust to debt, forcing monetary accommodation). @davig2011 extended this to regime-switching models, and @cochrane2011 applied the framework to the post-2008 environment.

@katagiri2020 connect demographics to fiscal dominance directly, showing in a calibrated model that aging can trigger a regime transition from monetary to fiscal dominance as pension obligations grow. @plantin2024 analyzes the implications of fiscal dominance for bank reserve requirements. However, these contributions are theoretical or focus on individual countries. No paper has tested the demographic-fiscal dominance nexus empirically across a broad cross-country panel.


# Data

## Sources and Construction

We construct a panel of 181 countries over 1990--2024 by merging data from three sources.

**Fiscal variables** are drawn from the IMF World Economic Outlook (April 2025 vintage, @imf2024weo). We extract six variables: government gross debt/GDP (GGXWDG_NGDP), government net debt/GDP (GGXWDN_NGDP), the primary balance/GDP (GGXONLB_NGDP), the cyclically-adjusted structural balance/GDP (GGSB_NPGDP), government revenue/GDP (GGR_NGDP), and government expenditure/GDP (GGX_NGDP). The structural balance is available for approximately 83 countries, concentrated among advanced and upper-middle-income economies.

**Demographic and macroeconomic variables** are drawn from our base panel, which integrates data from ten international sources following the methodology described in our companion paper. Key variables include the Fair-Dominguez demographic polynomials ($Z_1$, $Z_2$, $Z_3$), the old-age dependency ratio (OADR), GDP per capita in PPP terms, real GDP growth, the Chinn-Ito capital account openness index [@chinnito2006], net foreign assets as a share of GDP, and health expenditure as a share of GDP.

**Interest rates** follow a hierarchy: 10-year government bond yields where available, then the policy rate, then the lending rate. This hierarchy is important because lending rates, available for a wider set of countries, are substantially higher on average (reflecting bank margins) and would bias upward any estimate of the interest-growth differential.

## Key Variables

The **output gap** is computed using the Hodrick-Prescott filter [@hodrickprescott1997] applied to log GDP per capita (PPP) for each country, with smoothing parameter $\lambda = 6.25$ (appropriate for annual data). This replaces the IMF's own output gap measure, which is available for only 27 countries in our sample, enabling estimation across the full 181-country panel.

The **government expenditure gap** is defined as the deviation of government expenditure/GDP from its country-specific mean, capturing transient fiscal shocks.

The **r-g differential** is computed as the nominal interest rate minus real GDP growth. We also compute a real version using the ex-post real interest rate (nominal rate minus CPI inflation).

All fiscal variables are winsorized at the 1st and 99th percentiles. The resulting panel contains 8,295 country-year observations, of which 5,568 have government debt data and 5,699 have primary balance data.

## Summary Statistics

| Variable | Mean | Std. Dev. | Min | Max | N |
|:--|--:|--:|--:|--:|--:|
| Government Debt/GDP (%) | 55.2 | 39.3 | 0.0 | 228.7 | 5,568 |
| Primary Balance/GDP (%) | -0.5 | 5.1 | -18.4 | 19.7 | 5,699 |
| Structural Balance/GDP (%) | -2.6 | 3.4 | -12.6 | 5.6 | 2,361 |
| r-g (nominal, pp) | 8.9 | 13.4 | -8.2 | 79.4 | 4,276 |
| r-g (real, pp) | 0.4 | 11.8 | -66.2 | 38.4 | 4,241 |
| Old-Age Dependency Ratio | 0.125 | 0.092 | 0.010 | 1.099 | 8,295 |
| Z_1 | -1.27 | 1.37 | -3.98 | 3.54 | 8,295 |
| Real GDP Growth (%) | 3.4 | 6.3 | -54.3 | 148.0 | 6,461 |
| KAOPEN | 0.20 | 1.56 | -1.94 | 2.28 | 5,807 |

The mean nominal r-g of 8.9 percentage points is driven by emerging and developing economies with high lending rates. Among OECD countries using bond yields, the median r-g is substantially lower (approximately 1--2 percentage points).


# The Bohn Fiscal Reaction Function

## Baseline Specification

We estimate the Bohn fiscal reaction function using pooled GLS with AR(1) error correction:

$$pb_{it} = \beta_0 + \beta_1 d_{i,t-1} + \beta_2 \tilde{y}_{it} + \beta_3 \tilde{g}_{it} + u_{it}$$

where $pb_{it}$ is the primary balance/GDP, $d_{i,t-1}$ is lagged government debt/GDP, $\tilde{y}_{it}$ is the HP-filtered output gap, and $\tilde{g}_{it}$ is the government expenditure gap. The key parameter is $\beta_1$: a positive value indicates that governments tighten fiscal policy in response to rising debt, satisfying the Bohn sustainability condition.

**Table 1: Bohn Fiscal Reaction Function Results**

| Model | $\beta_1$ (debt_lag) | SE | p-value | N | Countries | $R^2$ |
|:--|--:|--:|--:|--:|--:|--:|
| (1) Baseline Bohn | 0.0054 | 0.0027 | 0.043 | 5,061 | 181 | 0.044 |
| (2) + Z levels | 0.0064 | 0.0027 | 0.018 | 5,061 | 181 | 0.052 |
| (3) + debt $\times$ Z interactions | 0.0037 | 0.0049 | 0.451 | 5,061 | 181 | 0.053 |
| (4) + debt $\times$ OADR | 0.0048 | 0.0040 | 0.232 | 5,061 | 181 | 0.046 |
| (5) + debt $\times$ Z $\times$ KAOPEN | 0.0057 | 0.0054 | 0.294 | 4,606 | 170 | 0.055 |
| (6) Structural Bohn | **-0.0113** | 0.0040 | **0.005** | 2,251 | 83 | 0.149 |

The baseline Bohn coefficient (Model 1) is positive and significant at the 5% level: a 10 percentage point increase in the debt ratio is associated with a 0.054 point improvement in the primary balance. This is a weak response---substantially smaller than the 0.02--0.05 range found in advanced-economy panels [@ghosh2013]---but statistically significant, providing a minimal sustainability result for the pooled global sample. To put this in context, $\beta \approx 0.005$ implies that a country with 100% debt/GDP generates only a 0.5 percentage point primary surplus from the Bohn reaction, and a country at 200% generates only 1.0 point. At any positive $r - g$, this reaction is too weak to stabilize debt; only when $r - g \leq 0$ (as in Japan under yield curve control) does debt converge to a finite equilibrium.

## Demographics Do Not Weaken the Bohn Coefficient

Model 2 adds the Fair-Dominguez demographic polynomials as levels. The Z variables are jointly significant (Z_1: +19.5, p = 0.002; Z_2: -2.7, p = 0.004; Z_3: +0.10, p = 0.007), and the Bohn coefficient strengthens slightly to 0.006. This means demographics affect the primary balance directly, but not through erosion of the fiscal reaction.

The critical test is Model 3, which interacts lagged debt with the demographic polynomials (debt $\times$ Z_1, debt $\times$ Z_2, debt $\times$ Z_3). If aging weakens the fiscal reaction function---the "fiscal fatigue through demographics" hypothesis---these interactions should be negative and significant. **They are not.** All three interaction terms have p-values above 0.41. Model 4 tests the simpler debt $\times$ OADR interaction and finds the same null (p = 0.737). Model 5 adds a triple interaction with KAOPEN to test whether financial openness mediates any demographic weakening of the Bohn coefficient; again, all interactions are insignificant (p > 0.25).

This is a meaningful negative result. Demographics do not erode fiscal discipline in the sense of weakening the government's responsiveness to debt. The mechanism through which aging threatens fiscal sustainability must lie elsewhere.

## The Structural Balance Reveals Active Loosening

Model 6 replaces the primary balance with the cyclically-adjusted structural balance as the dependent variable. The structural balance strips out automatic stabilizers (cyclical revenue fluctuations, unemployment insurance), isolating the discretionary fiscal stance. This model is available for 83 countries with structural balance data.

The result is striking: the Bohn coefficient reverses sign to **-0.011 (p = 0.005)**. Governments with higher debt run *looser* discretionary fiscal policy. This finding---that the primary balance weakly stabilizes debt only because automatic stabilizers do the work, while discretionary fiscal policy moves in the opposite direction---is consistent with the "fiscal fatigue" interpretation of @ghosh2013, but more severe: it implies that discretionary fiscal policy is procyclical with respect to debt levels.

To confirm this is not a sample composition effect, we estimate both the primary and structural Bohn regressions on the identical 82-country subsample where both measures are available (Table A1 in the appendix). The primary Bohn coefficient on this restricted sample is 0.010 (p = 0.001), while the structural coefficient is -0.006 (p = 0.061). The sign reversal is preserved on the identical sample, confirming that automatic stabilizers account for the apparent sustainability in the primary balance.

The sign reversal of the structural Bohn coefficient is robust to alternative output gap constructions: all four specifications (HP filter, IMF WEO gap, Hamilton filter, growth+inflation controls) produce negative structural coefficients (-0.005, -0.009, -0.003, -0.003 respectively). However, statistical significance is sensitive to gap measurement and sample: the HP and IMF gaps yield marginal significance (p = 0.084 and 0.100), while the Hamilton and growth+inflation specifications are not significant at conventional levels (p = 0.324 and 0.343). The robust stylized fact is the sign reversal itself---discretionary fiscal policy loosens as debt rises---though the precision of the estimate depends on how the output gap is measured.

### Why Does the Structural Balance Reveal Pro-Cyclicality?

The reversal from a positive primary-balance Bohn coefficient to a negative structural-balance coefficient demands explanation. The structural balance strips out two components: (i) cyclical revenue fluctuations (tax receipts that rise and fall with the business cycle) and (ii) cyclical expenditure fluctuations (primarily unemployment insurance). What remains is the discretionary fiscal stance — the policy choices governments make independent of economic conditions.

The negative structural Bohn coefficient implies that as debt rises, governments *expand* discretionary spending or *cut* discretionary taxes. This is not primarily driven by one-off emergency measures (COVID stimulus, banking bailouts), which would appear as outliers rather than a systematic negative coefficient across 83 countries and 34 years. Rather, it reflects the structural ratchet effect of entitlement programs. As populations age, pension obligations and social transfer commitments become legally binding expenditure that expands automatically with the eligible population. Governments treat these commitments as non-discretionary — politically, they are — but the IMF's cyclical adjustment does not classify them as automatic stabilizers. They appear in the structural balance as discretionary spending that grows with debt-financed demographic commitments.

The mechanism is therefore: aging → higher pension/transfer obligations → governments finance these by borrowing rather than by raising taxes or cutting other spending → the structural balance deteriorates as debt rises → the Bohn coefficient turns negative. This is not fiscal irresponsibility in the conventional sense; it is the fiscal consequence of entitlement structures designed for younger populations being applied to older ones. The structural Bohn reversal is, in effect, the demographic fiscal gap (Section 5) manifesting as apparent policy pro-cyclicality.

## Rolling-Window Evidence

To examine temporal stability, we estimate the Bohn coefficient in rolling 15-year windows.

**Table 2: Rolling Bohn Coefficient Over Time**

| Window | $\beta_1$ | p-value | Countries |
|:--|--:|--:|--:|
| 1990--2004 | -0.006 | 0.065 | 170 |
| 1994--2008 | 0.000 | 0.975 | 179 |
| 2000--2014 | 0.007 | 0.035 | 181 |
| 2003--2017 | 0.012 | 0.002 | 181 |
| 2006--2020 | 0.013 | 0.001 | 181 |
| 2008--2022 | 0.004 | 0.308 | 181 |
| 2010--2024 | 0.003 | 0.489 | 181 |

The Bohn coefficient displays a clear arc. It was negative in the 1990s (debt accumulation in post-Soviet transition, Asian crisis), turned positive during the 2001--2018 era of fiscal consolidation in advanced economies and commodity booms in developing ones, and has collapsed to insignificance since windows including 2020 or later. The COVID-19 pandemic and its fiscal aftermath have effectively eliminated the pooled fiscal reaction function. This pattern is consistent with the broader narrative of post-crisis fiscal deterioration documented in our companion paper on rolling demographic-current account stability.


# The Expenditure-Revenue Asymmetry

## Core Decomposition

If demographics do not weaken the Bohn coefficient, how does aging threaten fiscal sustainability? We decompose the fiscal gap by estimating separate regressions of government expenditure/GDP and government revenue/GDP on demographics.

**Table 3: Expenditure and Revenue Decomposition (OADR)**

| Dependent Variable | OADR Coefficient | SE | p-value | $R^2$ | N |
|:--|--:|--:|--:|--:|--:|
| Government Expenditure/GDP | +126.3 | 19.0 | < 0.001 | 0.410 | 3,776 |
| Government Revenue/GDP | +38.2 | 20.1 | 0.058 | 0.477 | 3,787 |
| Fiscal Gap (Exp. - Rev.) | +55.5 | 10.3 | < 0.001 | 0.067 | 3,776 |

The expenditure sensitivity is 3.3 times the revenue sensitivity. OADR is measured as a fraction (0.10 = 10%), so the coefficients refer to unit changes in this fraction. At the sample mean OADR of 12.5%, the marginal effect of a 1 percentage point OADR increase is approximately +0.87 points on expenditure/GDP and +0.43 points on revenue/GDP. A 10 percentage point increase in the OADR from the sample mean implies approximately +7.2 points of expenditure/GDP but only +4.5 points of revenue/GDP, opening a fiscal gap of approximately 2.7 points of GDP. This asymmetry is the core mechanism through which demographics threaten fiscal sustainability. The revenue sensitivity is only marginally significant (p = 0.058), reflecting the difficulty of detecting revenue responses to aging across a heterogeneous global panel; the expenditure channel is unambiguous.

Both the expenditure and OADR relationships display diminishing returns: the quadratic terms on OADR are negative and significant (expenditure OADR$^2$: -155.5, p = 0.002; revenue OADR$^2$: not significant). This implies that the fiscal cost of aging is largest for countries transitioning from low to moderate OADR (marginal effect at 5% OADR: +11.1pp per unit; at 25%: +4.9pp per unit), rather than for already-aged societies like Japan.

### Why Does Revenue Lag Expenditure?

The 3.3:1 expenditure-to-revenue sensitivity (+126.3 vs. +38.2 per unit OADR) demands explanation. Three mechanisms contribute.

**First, the shrinking labor tax base.** Government revenue in most countries depends heavily on labor income taxes and social security contributions, which together account for 50–70% of total revenue in OECD economies. As the working-age population shrinks relative to dependents, the tax base contracts mechanically. Consumption taxes partially offset this — retirees consume — but at lower rates than workers, and many essential goods (food, healthcare) are zero-rated or reduced-rate in VAT systems. Property and capital gains taxes grow with asset prices, which our companion asset returns paper shows are not demographically driven (equity cap/GDP is null with respect to Z). The net effect is that the revenue base grows more slowly than the population it must support.

**Second, political economy constraints.** Raising taxes on a shrinking workforce to fund a growing retiree population is among the most politically difficult fiscal adjustments. Median voter models predict that as the electorate ages, political support for tax increases declines while support for entitlement spending rises — the "gerontocracy" problem [@galasso2006]. Even where governments attempt revenue mobilization, aging societies tend to resist: Japan's consumption tax has been raised only twice in 30 years (from 3% to 10%), each time generating significant political backlash and economic disruption. The revealed preference of aging democracies is to finance the gap through borrowing rather than taxation.

**Third, the composition of new expenditure.** The spending driven by aging — pensions, long-term care, social transfers — is heavily transfer-based rather than service-based. Transfer spending generates limited multiplier effects and therefore limited induced tax revenue. A dollar of pension spending flows to a retiree who saves a portion and spends the rest on consumption with moderate tax incidence. By contrast, a dollar of infrastructure spending generates construction employment, corporate profits, and cascading consumption, each taxed at various points. The aging expenditure mix is therefore inherently less revenue-generating per unit than the spending it displaces.

## Health vs. Non-Health Spending

A common assumption is that healthcare costs are the primary fiscal burden of aging. We test this by decomposing government expenditure into health and non-health components for the 135 countries with health expenditure data.

**Table 4: Health vs. Non-Health Expenditure (OADR)**

| Component | OADR Coefficient | SE | p-value | Share of Total |
|:--|--:|--:|--:|--:|
| Health Expenditure/GDP | +23.1 | 3.7 | < 0.001 | 18% |
| Non-Health Expenditure/GDP | +103.8 | 18.4 | < 0.001 | 81% |
| Total Expenditure/GDP | +128.5 | 20.1 | < 0.001 | 100% |

Non-health expenditure---predominantly pensions and social transfers---accounts for approximately 80% of the demographic spending pressure. Health spending, while significant, is the junior partner. This finding has direct policy implications: healthcare reform alone, while important, addresses only one-fifth of the demographic fiscal burden. Pension reform is the critical lever.

## Pension Reform Interaction

We test whether countries that have implemented major pension reforms (raising retirement ages, shifting to defined-contribution systems, or tightening benefit formulas) exhibit lower expenditure sensitivity to aging. Using a dummy for 16 countries with documented reforms, we interact the OADR with the reform indicator.

The reform interaction is directionally correct---reducing the expenditure sensitivity by approximately 12 percentage points---but statistically insignificant (p = 0.47). This null likely reflects both the small number of reform countries and the fact that most reforms are recent, with their fiscal effects not yet fully realized. The Bohn coefficient interaction with reform is similarly insignificant (p = 0.27). Pension reform may matter, but its effects cannot yet be detected in the cross-country data.


# The Interest Rate Channel

## Theoretical Expectation

A large theoretical literature predicts that aging depresses the natural rate of interest [@carvalho2016; @rachel2017]. If this effect outpaces the reduction in potential growth, r-g falls and debt dynamics improve; if growth falls faster, r-g rises and debt sustainability worsens. The net effect is theoretically ambiguous.

## Empirical Results

We estimate the effect of demographics on rates, growth, and r-g separately.

**Table 5: Demographics and r-g Dynamics (mixed rate measures; see Appendix A3 for homogeneous yields)**

| Dependent Variable | Z_1 Coeff. | p-value | N | Countries | $R^2$ |
|:--|--:|--:|--:|--:|--:|
| Interest Rate (level) | -55.6 | 0.001 | 3,161 | 135 | 0.147 |
| Real GDP Growth | -7.0 | 0.209 | 4,239 | 164 | 0.047 |
| r-g (nominal) | -14.8 | 0.441 | 3,044 | 129 | 0.106 |
| r-g (real rate version) | +33.5 | 0.039 | 3,012 | 129 | 0.047 |

*Note: Interest rates follow a hierarchy (10-year bond yields where available, then policy rate, then lending rate). See Appendix Table A3 for results on the homogeneous 23-country bond yield subsample.*

Demographics strongly predict interest rate levels (Z_1 = -55.6, p = 0.001), but the effect on growth is weaker and no longer significant at conventional levels (Z_1 = -7.0, p = 0.209). In the nominal r-g specification, the effects approximately cancel (Z_1 = -14.8, p = 0.441). However, the real r-g version yields a positive and significant coefficient (Z_1 = +33.5, p = 0.039), suggesting that demographics may raise real interest rates relative to growth---an unfavorable sign for debt dynamics. **We interpret the r-g evidence as mixed**: the nominal specification and the homogeneous bond yield sample (below) show no significant effect, while the real version suggests a possible adverse channel. This pattern holds across pre- and post-GFC subsamples, high and low income countries, and across alternative rate measures for the nominal specification.

To address the concern that heterogeneous rate measures (mixing bond yields with lending rates) may obscure the r-g relationship, we re-estimate on a homogeneous sample of 23 countries with 10-year government bond yields (N = 635). On this sample, demographics significantly predict both yields (Z_1 = 53.1, p = 0.011) and growth (Z_1 = 35.6, p = 0.006), but the r-g regression remains insignificant (Z_1 = 20.1, p = 0.477). The r-g regression constitutes a direct test of $H_0: \beta_{rate} = \beta_{growth}$; the approximate test statistic is $t = 0.72$ ($p = 0.47$), confirming that the rate and growth effects are not statistically distinguishable on this clean sample.

The OADR spline specification (knots at 15%, 20%, 25%, 30%) produces no significant thresholds---there is no OADR level at which r-g detectably shifts. The high-debt interaction (Z $\times$ high_debt) produces no significant interaction effects.

This is perhaps the most important result in the paper. The theoretical literature on demographics and secular stagnation has focused heavily on the r channel, but our cross-country evidence suggests that for debt sustainability purposes, the nominal r and g effects approximately cancel, and even the real r-g effect (while significant in the broader sample) is modest compared to the expenditure channel. **The fiscal threat from aging operates primarily through the spending channel, not the interest rate channel.**

## Reconciling with the Secular Stagnation Literature

Our finding of no robust demographic effect on r-g appears to contradict @rachel2017, who attribute roughly 90 basis points of the secular decline in global real rates to demographics, and @carvalho2016, who model aging as depressing the equilibrium rate through lifecycle savings. The resolution lies in what these papers measure versus what we test.

Rachel and Smith (2017) and the broader secular stagnation literature (Summers 2014) estimate the effect of demographics on the *level* of interest rates, finding that aging lowers r. We confirm this strongly: Z_1 on the interest rate level is -55.6 (p = 0.001). The question for fiscal sustainability, however, is not whether r falls but whether r falls *faster than g*. Our nominal r-g evidence says the effects approximately cancel (Z_1 = -14.8, p = 0.44), though the real r-g specification shows a marginally significant positive effect (Z_1 = +33.5, p = 0.039). Demographics depress rates substantially (-55.6) while the growth effect is smaller and insignificant (-7.0, p = 0.21), and the net nominal r-g effect is indistinguishable from zero.

This cancellation is not mechanically obvious. The r channel operates through lifecycle savings (more retirees drawing down savings → lower capital supply → eventually higher r; but also more pre-retirees saving → higher supply → lower r), while the g channel operates through labor force shrinkage and reduced dynamism. That these two theoretically distinct channels produce offsetting effects on debt dynamics is an empirical finding, not a theoretical prediction.

Three factors explain the pattern. First, **sample composition**: Rachel and Smith estimate on 20 advanced economies where bond markets exist, monetary policy is conventional, and the r channel is cleanly identified. Our 181-country panel includes 100+ economies where "interest rates" are lending rates reflecting banking margins, not demographic fundamentals. On our homogeneous 23-country bond yield sample, where both yields and growth are significantly predicted by demographics (Z_1 = 53.1 and 35.6, p = 0.011 and 0.006), the r-g regression remains insignificant (Z_1 = 20.1, p = 0.48). The formal equality test ($t = 0.72$, $p = 0.47$) cannot reject that demographic effects on rates and growth are equal. Second, **monetary policy intervention**: quantitative easing, yield curve control, and forward guidance in aging economies (Japan, Eurozone, US post-2008) have compressed r below its demographic equilibrium, weakening the cross-sectional signal. Our companion asset returns paper confirms that demographics predict 10-year bond yields (Z_1 = 45.6, p = 0.011) in the OECD --- but this is a *level* effect that does not translate into r-g when g falls similarly. Third, **the Carvalho channel is OECD-specific**: our bilateral gravity paper documents that 58% of the demographic effect on capital flows operates through the interest rate channel, but only in OECD economies with deep bond markets. In a global panel, this channel is diluted to insignificance.

The policy implication is clear: whether or not demographics eventually move r-g in either direction, the fiscal threat operates *now* through the spending channel. Waiting for r-g resolution is not a viable strategy when the expenditure-revenue gap is already 7.2 points of GDP per 10pp of OADR.


# Debt Dynamics and Forward Projections

## Direct Demographic Effect on Debt

Beyond the expenditure-revenue decomposition, we test whether demographics predict annual changes in the debt-to-GDP ratio directly:

$$\Delta d_{it} = \gamma_0 + \gamma_1 Z_{1,it} + \gamma_2 Z_{2,it} + \gamma_3 Z_{3,it} + \delta d_{i,t-1} + \theta X_{it} + u_{it}$$

The Z_1 coefficient is +20.6 (p = 0.005), indicating that aging countries accumulate debt faster even after controlling for the fiscal balance, interest rates, and growth. This is consistent with demographics being strongly associated with debt accumulation through the fiscal gap channel documented in the previous section.

## Country-Specific Debt Trajectories

We simulate forward no-policy-change mechanical debt paths for 15 major economies through 2040, using the debt accumulation identity:

$$d_{t+1} = (1 + r_t - g_t) d_t - pb_t$$

where both $r_t - g_t$ and the fiscal gap are projected from estimated demographic coefficients using UN medium-variant population projections. These are **no-policy-change mechanical paths, not forecasts**: they do not model fiscal reaction functions, inflation surprises, monetary policy regime shifts, or the political economy of fiscal adjustment. Their purpose is to quantify the fiscal pressure that demographics create under current policy structures. We report three scenarios: (i) a no-reaction baseline where the fiscal gap evolves mechanically with demographics; (ii) a stylized Bohn reaction ($\beta = 0.005$) where the primary balance improves by 0.05pp for each 10pp of debt above the 2024 level; and (iii) a stronger reaction ($\beta = 0.02$) representing more aggressive fiscal consolidation. Projected debt is floored at 0% of GDP; values reaching the floor represent mechanical net-asset outcomes under the assumed path. Uncertainty bands (10th--90th percentile) are derived from 500 Monte Carlo draws from the estimated coefficient distributions.

**Table 6: Projected Debt-to-GDP Ratios, No-Policy-Change Scenario (median [p10, p90])**

| Country | 2024 | 2030 | 2035 | 2040 |
|:--|--:|--:|--:|--:|
| JPN | 248 | 442 [98, 500] | 500 [18, 500] | 500 [0, 500] |
| ITA | 144 | 210 [63, 417] | 294 [0, 500] | 399 [0, 500] |
| USA | 139 | 307 [177, 393] | 500 [140, 500] | 500 [105, 500] |
| FRA | 126 | 241 [67, 369] | 406 [31, 500] | 500 [0, 500] |
| GBR | 115 | 240 [82, 348] | 423 [63, 500] | 500 [43, 500] |
| CHN | 104 | 238 [133, 301] | 399 [112, 500] | 500 [77, 500] |
| BRA | 100 | 227 [78, 292] | 238 [174, 458] | 388 [179, 500] |
| IND | 91 | 199 [67, 260] | 381 [63, 500] | 500 [61, 500] |
| DEU | 71 | 118 [21, 235] | 156 [0, 500] | 193 [0, 500] |
| MEX | 67 | 144 [52, 204] | 270 [55, 445] | 500 [60, 500] |

Under the strong Bohn reaction ($\beta = 0.02$), median trajectories are substantially lower: the US reaches 417% (vs. 500% under no reaction), France stabilizes near 332%, and Germany remains below 182%. However, even with the strong reaction, most countries' median projections exceed 200% by 2040, underscoring that realistic policy reactions cannot fully offset the demographic fiscal gap.

Several patterns emerge from the no-reaction scenario:

**Rising trajectories.** The United States, United Kingdom, France, China, and India all reach or approach the 500% cap by 2040 in the no-reaction median, reflecting the compounding of demographic fiscal gaps with positive r-g differentials. These are no-policy-change mechanical paths and should be interpreted as the fiscal pressure that must be offset by policy adjustment, not as predictions.

**Wide uncertainty.** The 10th--90th percentile bands are wide, reflecting genuine uncertainty in both the fiscal gap and r-g coefficients. For most countries, the 10th percentile path remains below 100% while the 90th percentile reaches the cap, indicating that the direction of debt dynamics depends critically on realized interest rates and growth.

**Moderate trajectories.** Germany and Korea show more moderate median paths (193% and 126% by 2040), reflecting their more favorable initial conditions and demographic trajectories.


# Robustness

## Subsample Stability

We re-estimate the key specifications (Bohn reaction function, r-g dynamics) across multiple subsamples.

**Table 8: Z_1 Coefficient Across Specifications**

| Specification | Z_1 Coeff. | p-value | N |
|:--|--:|--:|--:|
| Bohn: Full sample | +25.6 | 0.003 | 5,061 |
| Bohn: Excluding Japan | -62.0 | 0.100 | 812 |
| Bohn: Excluding CCA | -78.3 | 0.026 | 846 |
| Bohn: OECD Only | -31.1 | 0.436 | 792 |
| Bohn: Europe | -84.8 | 0.051 | 661 |
| Bohn: Net Debt | -82.1 | 0.010 | 752 |
| Bohn: Structural Balance | -67.4 | 0.033 | 834 |
| r-g: Full sample | -14.8 | 0.441 | 3,044 |
| r-g: OECD Only | -48.3 | 0.189 | 879 |
| r-g: Emerging Markets | -9.0 | 0.706 | 2,165 |

The absence of a robust demographic effect on r-g holds across all subsamples: we do not find that demographics significantly predict r-g in any country group or with any rate measure. The Bohn Z_1 coefficients are more variable across subsamples but generally negative in restricted samples (OECD, Europe, CCA exclusion, net debt), suggesting that among advanced economies, aging is associated with *worse* primary balances conditional on debt levels.

## Alternative Rate Measures

| Rate Measure | Z_1 on r-g | p-value |
|:--|--:|--:|
| Bond Yield | +20.1 | 0.477 |
| Policy Rate | +16.4 | 0.475 |
| Lending Rate | -14.0 | 0.529 |
| Real Bond Yield | -7.7 | 0.763 |

We do not find robust evidence that demographics move r-g under any nominal rate measure. The main-sample results in Table 5 use mixed rate measures (10-year yields where available, then policy rates, then lending rates); the homogeneous 23-country bond yield sample is reported in Appendix Table A3. All Z_1 coefficients on nominal r-g are insignificant regardless of rate measure (all p > 0.47), providing consistent evidence that the rate and growth effects approximately cancel.

## Net Debt

Using net debt (gross debt minus financial assets) instead of gross debt in the Bohn regression produces a negative Bohn coefficient (-0.011, p = 0.373) and stronger demographic effects (Z_1: -82.1, p = 0.010 on the interaction). The net debt results are consistent with the structural balance finding: governments' asset positions do not offset the spending pressure from aging.

## Pension Spending Control

Adding OECD pension spending/GDP as a control in the Bohn regression (25 countries) absorbs much of the demographic signal but renders the pension variable itself highly significant (-0.45, p < 0.001): each additional percentage point of pension spending/GDP worsens the primary balance by 0.45 points, confirming the expenditure channel identified in our decomposition.


# Conclusion

This paper tests whether population aging undermines fiscal sustainability using the Bohn fiscal reaction function framework across 181 countries. Our findings overturn several assumptions in the theoretical literature.

**The r-g channel is not a robust threat.** Despite substantial theoretical attention to the effects of demographics on the natural rate of interest and the r-g differential, our cross-country evidence---including on a homogeneous 23-country sample with 10-year bond yields---shows that the nominal r-g effect is indistinguishable from zero. The real r-g specification yields a marginally significant positive effect, but this is not robust across rate measures or subsamples. The fear that aging will trigger a secular rise in r-g and initiate debt spirals is not robustly supported by the cross-country data.

**The spending channel is the core mechanism.** Aging raises government expenditure 3.3 times faster than revenue, opening a persistent fiscal gap that is strongly associated with debt accumulation. This gap is 80% non-health spending---primarily pensions and social transfers---contradicting the common emphasis on healthcare costs as the primary fiscal burden of aging.

**Fiscal discipline is weaker than it appears.** The Bohn coefficient is positive in the primary balance but negative in the structural balance---a sign reversal that is robust across gap measures, though statistical significance varies with the output gap construction. This pattern is consistent with automatic stabilizers doing the work of debt stabilization while discretionary fiscal policy loosens as debt rises. Rolling-window estimation shows that even this minimal fiscal discipline has collapsed since 2020.

**The window for reform is closing.** No-policy-change mechanical projections through 2040, with Monte Carlo uncertainty bands and stylized Bohn reactions, show that most major economies face rising debt trajectories. Even with a moderately aggressive policy reaction ($\beta = 0.02$), median debt paths for the US, UK, France, and China exceed 200% by 2040.

These results have direct policy implications. First, pension reform---not healthcare reform---is the primary fiscal lever for aging societies. Second, the interest rate environment is a sideshow for debt sustainability; what matters is the fiscal gap between age-related spending and revenue. Third, the erosion of the Bohn coefficient since 2020 suggests that the post-pandemic fiscal regime may represent a structural break in fiscal discipline, making the demographic projections presented here conservative.

Japan's trajectory offers a cautionary ambiguity. Its negative r-g (-0.7%) means that debt ratios will eventually decline mechanically, regardless of the fiscal stance---but only after decades of stagnation and deflation. Whether "Japanification as its own cure" represents a desirable outcome for other aging societies is, at best, debatable.


# References
